OFFSET
0,7
COMMENTS
The usual policy in the OEIS is not to include such "doubled" sequences. This is an exception. - N. J. A. Sloane
Based on the morphism 1->{5}, 2->{6}, 3->{4}, 4->{2}, 5->{3}, 6->{1, 6}.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Sergio Falcon, Generalized (k,r)-Fibonacci Numbers, Gen. Math. Notes, 25(2), 2014, 148-158.
I. Wloch, U. Bednarz, D. Bród, A Wloch and M. Wolowiec-Musial, On a new type of distance Fibonacci numbers, Discrete Applied Math., Volume 161, Issues 16-17, November 2013, Pages 2695-2701.
Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,1).
FORMULA
a(n) = a(n-2) + a(n-6), starting 1,1,1,1,1,1.
G.f.: (1+x)/(1-x^2-x^6).
MATHEMATICA
s[1] = {5}; s[2] = {6}; s[3] = {4}; s[4] = {2}; s[5] = {3}; s[6] = {1, 2}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] a0 = Table[Length[p[i]], {i, 0, 50}]
m = 6; For[n = 0, n < m, n++, a[n] = 1]; For[n = m, n < 51, n++, a[n] = a[n - m] + a[n - 2]]; Table[a[n], {n, 0, 50}] (* Sergio Falcon, Nov 12 2015 *)
CoefficientList[Series[(1 + x) / (1 - x^2 - x^6), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 1, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1}, 60] (* Vincenzo Librandi, Jan 19 2016 *)
PROG
(PARI) x='x+O('x^55); Vec((1+x)/(1-x^2-x^6)) \\ Altug Alkan, Nov 10 2015
(Magma) I:=[1, 1, 1, 1, 1, 1]; [n le 6 select I[n] else Self(n-2)+Self(n-6): n in [1..60]]; // Vincenzo Librandi, Jan 19 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Jun 03 2005
EXTENSIONS
Edited by N. J. A. Sloane, Dec 01 2006
STATUS
approved